Bid the Market

 

Hedge Systems, Inc

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Evaluation Date: Steps: Sequence Length: Ticker:

 

In the past several years, the equity achieves great return and huge volatility. Portfolio managers and individual investors want to bid the market and reduce the volatility.

 

In the past year, the growth concentrated in the new technology, such as Internet, Communication. The majority of the stock is in the negative area. The market would be a bear market without the new Technology section.

 

The traditional method to select stock and track the index was very poorly. Most of the growth fund did not bid the index.

 

In this paper, we outline a methodology to select stock.

 

1.     The market

 

In the following graph, we assume invest $100 at five indexes, Dow Jones Industry Average(^DJI), NAS/NMS COMPSITE(^IXIC), S&P 100 INDEX(^OEX), S&P 500 INDEX(^SPX) and RUSSELL 2000(^RUT). The result at 3/26/99 is Dow Jones $124.757
, NAS/NMS COMPSITE is 152.1357. S&P 100 INDEX is 131.0852. S&P 100 INDEX is 138.4705 and RUSSELL 2000 is 91.33106. At same period,

 


At Same Period, WCOM increase 285.32 percent. Microsoft (MSFT) increase 258.50 percent and American on Line (AOL) increase 1048.76 percent.

 

In the past year, the broad market is far behind. The growth is concentrated a handsome of new technologies. Though there is a probability that the broad market may drag down the growth of the high flied securities, there are higher chances the fly will continue due to worldwide recovery.

 

Regression model is widely used in the process to select stocks. However, it seems less successful in recent years. We intend to improve the regression model to fit the current market conditions. First we select a set of indexes that we think better reflect the current market conditions. Then we create multiple step regression models to adapt the markets. As the result, we estimate the parameter a, which represents the daily excess return over the market for specified securities. To compare the return, we define the risk-adjusted return as ration of the excess return over the specific volatility.

 

2.     Select Indexes

 

To reflect the behavior of the markets, we should select different set of indexes. We select the following set of indexes.

 

Ticker

Description

^BIX

S&P BANKINDEX

^CWX

CBOE COMPSFTWR

^DJI

DJ INDUAVERAGE

^DRG

PHARMCEUTICLNDX

^HCX

S&P HLTHCARE

^INX2

INTERNET INDEX

^IUX

S&P INSURANCE

^IXIC

NAS/NMS COMPSITE

^MSH

MSTAN HITECH

^OEX

S&P 100INDEX

^OIX

OIL INDEX

^RLX

S&P RETAILNDX

^RUT

RUSSELL 2000

^SPX

S&P 500  INDEX

^VIX

MKTVOLTLTY NDX

^XAL

AIRLINE INDEX

^XBD

SEC BROKER DEALR

^XCI

COMPUTER TECH

 

The internet index and CBOE Computer Software Index reflect the most active sector on the market. The Market Volatility Index gives the short posture of the markets.

 

 

 

3.     The model

 


We assume the price of equity follows a lognormal model. In other works the return follows the normal model. The current return is a liner combination of past m steps of the index returns. Mathematically, we can write the equity return as

 

 


Where X(k,i-l) is the index k return at time i-l.

 


Suppose we observed a sequence of returns of the index and the equity. The coefficient a and b can be identify by making the noise as small as possible. Mathematically, we will solve the following problem:

 


The above problem is called adapted parameter identification problem. There are several method can solve above equations.

 

The following graph shows the project prices and actual market prices. The length of time sequence is 300 day. The delay period is 2.


 

 


4.     Adjusted Excess Return

 

Parameter a represents the daily excess return of the equity with respect to the market. The specific volatility s represents the volatility which can not explained by the market.  Since the risk level is different, the return of different equity can not compare each other. Therefore we define the risk adjusted excess adjusted return as the ration of a and s. Mathematically,

 

Risk Adjusted Excess Return m

 


 

 


The following table shows the excess return, specific volatility and risk adjusted excess returns.

 


 


In above table, The AOL and MSFT has the highest Risk Adjusted Return. The excess return of YHOO is higher than Microsoft. However the specific volatility is much higher than Microsoft. Consequently, the risk-adjusted return are lower than Microsoft.

 

 

5.     Value at Risk

 

The above model can be used as value at risk. The sum of b is the sensitivity of the security with respect to the indexes.

 

To evaluate the value at risk of a equity, we can decompose the risk into the market risk and the specific risk. The market risk can further divided into the risk due to different indexes.

 

6.     Assets allocations

 

The risk adjusted excess return can be the basis of assets allocation. We suggest to hold a portfolio with the ratio proportion to the risk adjusted excess return.

 

Suppose we have $100, we will invest our money into the following portfolio as 3/26/99.

 

                                   

AOL

24.16878

MSFT

18.4713

YHOO

8.698968

BA

3.235848

IBM

7.512935

ATHM

6.521202

DELL

12.28776

WCOM

19.1032